Theorem necom 2486

Description: Commutation of inequality. (Contributed by NM, 14-May-1999.)

Assertion

Ref	Expression
necom	|- ( A =/= B <-> B =/= A )

Proof of Theorem necom

Step	Hyp	Ref	Expression
1		eqcom 2233	. 2 |- ( A = B <-> B = A )
2	1	necon3bii 2440	1 |- ( A =/= B <-> B =/= A )

Syntax hints:   <-> wb 105   =/= wne 2402

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-5 1495  ax-gen 1497  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-ne 2403

This theorem is referenced by:  necomi  2487  necomd  2488  difprsn1  3812  difprsn2  3813  diftpsn3  3814  fndmdifcom  5754  fvpr1  5859  fvpr2  5860  fvpr1g  5861  fvtp1g  5863  fvtp2g  5864  fvtp3g  5865  fvtp2  5867  fvtp3  5868  netap  7476  2omotaplemap  7479  zltlen  9561  nn0lt2  9564  qltlen  9877  fzofzim  10431  flqeqceilz  10584  isprm2lem  12709  prm2orodd  12719  tridceq  16720